Find Puv for v= (1,2,3) and U= span((9,1,5)) in V= R3.
linear alegbra
Let u, v, w be linearly independent vectors in R3. Which statement is false? (A) The vector u+v+2w is in span(u + u, w). (B) The zero vector is in span(u, v, w) (C) The vectors u, v, w span R3. (D) The vector w is in span(u, v).
Question 1 2 pts Describe the span of {(1,0,0),(0,0,1)} in R3 The x-z plane R3 R2 The x-y plane Question 2 2 pts Describe the span of {(1,1,1),(-1,-1, -1), (2,2, 2)} in R3 A plane passing through the origin Aline passing through the origin R3 A plane not passing through the origin A line not passing through the origin Question 3 2 pts Let u and v be vectors in R™ Then U-v=v.u True False Question 4 2 pts Ifu.v...
Consider the subspaces U=span{[4 −2 −2],[10 1− 4]} and W=span{[3 −4 −1],[10 2 −2]}.Find a matrix X∈V such that U∩W=span{W}.
Find a linear mapping F your answer. R3 R3 whose image is spanned by (1,2,3) and (4,5,6). Explain
2) Let Let T : R3 - R3 such that T(ij) ,, j 1,2,3. Find the matrix A associated to T in the canonical basis. Find a basis of its kernel and its image. Verify your answers.
2) Let Let T : R3 - R3 such that T(ij) ,, j 1,2,3. Find the matrix A associated to T in the canonical basis. Find a basis of its kernel and its image. Verify your answers.
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap The following statements are equivalent. 1. ai,a2,..,a, span R" = # of rows of A. 2. A has a pivot position in every row, that is, rank(A) Select one: Oa. No since rank([uv]) < 2 3=# of rows of the matrix [uv b.Yes since rank([uv]) =2 = # of columns of...
Let u = (2,-1,1), v= (0,1,1) and w = (2,1,3). Show that span{u+w, V – w} span{u, v, w} and determine whether or not these spans are actually equal.
Find the distance from the vecto to the subspace W = Span{u, v} where 3 -1 | 1 |, and = | 113 11 2 ○ 16 1 옳
0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V)
0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V)
Let T: R3 → R3 be the linear transformation that projects u onto v = (9, -1, 1). (a) Find the rank and nullity of T. rank nullity (b) Find a basis for the kernel of T.